On the forces on a cutter suction dredger in waves

(1)

J

i

Bibliotheek van de

Afe!g Scheesbouv- e

Tehi

e oc! e', Cet

DCU-

ÌATiE DATUMI

ON THE FORCES ON A CUTTER SUCTION DREDGER IN WAVES

J.E.W. Wichers

- Netherlands Ship Model Basin Wageningen

THE NETHERLANDS

ABSTRACT

This paper deals with the behaviour of a cutter suction dredger waves. It-is well known that a conventional cutter suction dredg-er can meet problems when it opdredg-erates in waves. When cutting hard soils, problems may arise due to impact loads on the cutter head. 'Problems may also arise as a result of the loads on the spud or the

spud carriage. The loads on the cutter head and on the spud are de-pendent on the sea condition and the restoring characteristics of the elements which restrain the wave induced motions. For a given dredger the restoring characteristics depend on the different phases of the dredging operation. In this respect two important phases can .be distinguished: i.e.

- the moored condition

j The dredger is restrained by the spud and by the cutter ladder

swing wires, while the ladder is raised for the replacement of the cutter head or for other reasons.

- the operational condition

The ladder is lowered and the cutter head is working in the breach.'

In this situation the dredger is restrained by the spud, by the ladder swing wires and by the cutter head itself. ¡

At the Netherlands Ship Model Basin (N.S.M.B.) model tests in regular waves were carried out with a cutter suction dredger in both

of the above mentioned conditions.

For the case of the moored condition with the dredger in head waves an existing method for the computation of hydrodyniic

coeffi-cients, wave loads an motions of floating bodies of arbitrary shape

was aPplied _{The results of the coñ-iput.tions have been compared with}

T'ne figures _{are presented at the end of the paper.}

(2)

)fl fl..:-t

the results of model tests. From the comparison it _{can be concluded} that the calculated motions of the dredger and the calculated _spud foràes agree well with the values measured on the model.

Results of the model tests simulating the operational condition are presented. The rèsuits give insight into the causes of high loads on the cutter head and the spud and the characteristics _{of the}

loads.

,- O?) t ¡

-'.

.

Some future efforts will be discussed with respect to the

pre-diction of the loads on the cutter head and on the spud in the

oper-ational condition.

INTRODUCTION

A conventional cutter suction dredger provided with _{a spud}

sys-teni will be considered. The spud causes a relatively stiff mooring system, which enables an accurate positioning of the cutter head and an increased productivity. Dredging is carried out by swinging the

dredger about a working spud resting in the sea bed. The dredger is

s1nrng from one side of the channel to the other by means of two

for-ward wires, operated from the twin drums of a central manoeuvring winch or from separate swing winches. The wires are usually led over guide pulleys mounted near the cutter head end _{of the cutter ladder.} The working spud is mounted on a carriage which runs in a longitudi-nal well in the after part of the vessel. The cutter _{suction dredger} with spud and spud carriage is shown in Figure 1.

During dredging operations two situations have to be considered

viz.:

Cutter head raised out of the breach: moored condition This can take place for several _{reasons, for instance:}

- The cutter ladder is raised above water for replacement of the

cutter head.

- Upon completion of the cut the curter ladder is raised. The dredger is advanced by moving the spud carriage and next the cutter is brought into position for the next sweep.

- At the end of the travel of the spud carriage the cutter ladder is raised. The dredger is swung into a position over the centre line of the channel, the auxiliary spud is lowered, the working spud raised and the carriage returned to the _{forward position.} The working spud is lowered, the auxiliary spud raised _{and the}

dredging operation can be continued.

During all of the above mentioned situations the motions of the dredger are restrained by means of the spud and the forward swing wires. This situation will be referred to _{as the moored condition.}

Cutter head working in the breach: operational _condition

During the dredging operation the cutter is working in the breach. By means of the swing wires a pre-tension is put on the cutting side of the cutter head. In this situation the dredger is re-strained by the spud, the forward swing wires _{and the cutter head} itself. This situation will be referred to as the operational

condition.

Both situations will occür under the same wave conditions. From the point of view of the restoring characteristics _{of the systems} these systems are quite different.

(3)

rduct.n hc:

In order to obtai insight in the operational limits the fol-lowing aspects of both systems will be studied in this paper and èompared for the case that the dredger is working in regular waves:

-the motions;

the mooring forces (spud force and forces on the cutter head). For this purpose model tests have been carried out in regular head and beam waves. The model tests were carried out for one simplified

soil condition, ne particular cutter suction dredger and for one

water depth.

In addition to model tests mathematical models can be used as an aid to study the influence of the mentiohed parameters on the mo-tions and the mooring forces (spud force and forces on the cutter head). Then mathematical models will be applied to dredgers the by-drodynamic reaction force coefficients, the wave exciting forces and the restoring force coefficients h.ve to be knorn in order to solve the equations of motion. The hydrodynamic coefficients and the wave

exciting forces on the dredger barge can be obtained by using the three-dimensional linear potential theory. In this study the N.S.M.B.

computer program DIFFRAC has been used, which has been applied suc-cessfully to various kinds of floating structures. More attention has to be paid to the restoring forces. Due to the excursion of the dredger restoring forces will occur. The restoring forces will be

caused by the hydrostatic properties and by the mooring system. The mooring restoring forces originate from the elastic properties of the spud, the cutter ladder and the swing wires as well as from the properties of the soil. For instance, for the spud connection to the sea bottom we can assume:

in a rocky sea bed and in compact sand: the spud point can be

as-sumed to act as a ball-joint connection;

- in softer soils: the spud will penetrate into the sea bed result-ing in a partly or totally clamped connection to the sea bed.

The restoring force due to the cutter impression in the breach in longitudinal, transverse and vertical direction will be a

func-tion of the soil properties. In general this restoring force will have non-linear and time dependent load-compression characteristics, while coming free from the breach the restoring force will be zero.

If the required soil data are available a description of a

mathemat-ical model can be established.

In this paper a description of the mathematical models will be given. The models concern head waves only. The equations of motion will be formulated according to:

- the frequency-domain description for linear systems; - the time-domain description for non-linear systems.

MODEL TESTS

General

For the model tests a conventional cutter suction dredger has been used. Both the moored and the operational condition have been tested. The test set-up is presented in Figu-e 3. The water depth

amounts to 21.3 in. The sea bottom was assumed to be rocky soil. The model tests were carried out on a scale of 1:32 in the ',-Tave and Cur-rent Laboratory of the T.S.r.LB. The model test data were

(4)

tre-;clu: shc.:

td in. ts piper arefor thé full scale.

;'bESCRIPTI0NOF:MODELS .

rans.

:Dredger.Barge..andCutterLadder.. ...

..-' 'Thbare dimensions are shown in Figure 2. The stability data of the dredger barge including the cutter ladder in horizontal

posi-:tion are as follows:

Draft (even keel) T 3.52 ni3

Displacement V = ₇₇₂ m

- Centre of gravity in height KG = 5.33 ni

Centre of gravity in length from A.P. AG 31i..88 ni

Transverse metacentric height G.M.1 = 5.79 ni

Longitudinal metacentric height GM = 116.75 m

- Longitudinal radius of inertia k 18. 7 m

yy Spud

The elasticity of the spud pole was simulated. The bending stiffness EI corresponds to 1,050,000 ton.m2. It was assumed that in hard soil the spud point acts as a ball-joint at the bottom. At the carriage the spud pole was vertically guided by a wheel system. The

spud guiding system and the spud connection at the sea bottoni are shown in Photographs No. 1 and 2.

Breach Simulation

By means of long wires in longitudinal and transverse direction the linear load compression characteristic of the breach was

simu-lated.

(5)

Z;

rupns.

n'

2i1

c3r(ect ion

!cre

Photograph No. 2: Spud connection at the sea

bottom (ball-joint)

when the cutter head comes out of the breach these wires be-come slack and when the wires will be under tension the load-com-pression characteristic will work. Each wire, including the strain

gauge force transducer, represents t.he assumed linear load/soil

corn-pression relationship The simulation of the breach is shown in Photograph No. 3.

f.L

Photograph No. 3: Simulation of the cutter head in the breach

htet

(6)

I

For the operational condition the cutter ladder hoisting wires were assumed to be a soft system. Therefore in the model the

hoist-ing wires were deleted.

...

. ...:.

Swing Side Wires.,.

_{:::-''. ...}

i ne po i n t

The elasticities of the starboard and port side swing wires

eré sinurated.Thelinearlóadelongation characteristic of each

line amounts to . ton/rn. In operational condition the pre-tensions

on the starboard and in the port side wire amount to and tons respectively.

Motions

The linear motions were measured at the origin of the system of co-ordinates, as indicated in Figure 3.

Test Program

During the test program the following signals were measured: Longitudinal and transverse spud force at the bottom connection. Longitudinal and transverse cutter forces.

The motions of the dredger. The forces in the swing wires.

The sign convention for the moored and operational condition

are shown in Figure 3.

The following program was carried out:

The results are presented in the Figures

8, 9,

10 and 12.

MOORED CONDITION

Computations

Due to the spud the system is relatively stiff, especially in longitudinal direction. For this kind of stiff mooring system the effect of the second order wave drift forces on the motions can be neglected. Because the wave drift foices are an order smaller than the first order wave forces, the motions of the dredger and the

Wave frequency in rad./sec. Wave period in sec. Wave direction 180 deg. Wave direction 210 deg. Moored condition Operational condition Operational condition 1.05 o.8 0.70 0.52 O.)42 6.0 1.5

9.0

12.0 15.0 2

mm

a 2 a inni 2 a

mm

1.05 0.88 -1.15 0.89

0.19

-0.77 0.61

0.91

0.19 -0.91

rductir

hct-t _{MODEL c''pr}

_-:

(7)

'5 r(1Jc '..'.

rQDEL

. :

- .

forces on. the spud and cutter head will be mainly determined by the first order wave forces and moments.

;1cJ

the restoring forces for the spud mooring have been linearized the equations of motion according to the frequency domain 'description have beenapplied'tothe moored conditions and solved.

As an' example the equation of motion based on Newton's law of dynam-ics for, the system with, one degree of freedom is given below:

m5 = -a (w) . - b (w) - c .x + F (w)sin(wt +

xx xx

H xx H xa x

Hydrodynamic Restoring Wave

reaction forces force exciting force

:fl

which: m = mass of the dredger

a(w) = added mass at frequency w

b(w) = potential damping at frequency w

c = linear restoring coefficient due to the

hyth-o-X

statics and the mooring system

F(w) = amplitude of the steady oscillatory wave excit-ing force at frequency w

phase angle with regard to wave elevation

These equations of motion can only be used as a description in the frequency domain of a steady oscillatory motion, since the

hydrody-namic coefficients a.. and b deDend on the frecuency of motion. In

xx xx

-general terms, for the dredger in head waves, the equations of

mo-tion for the surge (x), heave (z) and pitch (0) momo-tion are as fol-lows (three degrees of freedom):

(m-1-a )+a .+a .0+b .+b .+b

_.é+

xx xz xE) xx xz xE)

+c .x+c .z+c .O=F

sin(wt+c

xx xz x® xa X a

.+(m+a )+a .®+b

±+b .+b

.6+

zx zz zO zx zz zO

+c .x+c .z+c .0=F

_zx

sin(wt+c

zz zO za + a0. + (I+a00).0 + b0.* + b0. + b0

+c .x+c .z+c .G=M

sin(wt+ Ox

Oz

0G Ga

in which: a = added mass in x-direction due to motion in

x-direc--xx

tion

a , a are coupled mass coefficients xz xO

b = potential damping in x-direction due to motion in xx

x-direction

b, b0 are coupled damping coefficients

c _{= spring coefficient in x-direction due to} displace-xx

ment in x-direction

c and c are coupled spring coefficients xz, xO

(8)

..,-mass of the dredger

.=rnoment of inertia of the dredger

For the computation of the hydrodynamic coefficientsand the wave exciting forces and moment a three-dimensional linear potential

diffraction theory has been used, using a singularity distribution, which is described by means of Green's functions. The computer pro-gram available at the N.S.M.B. is described in Ref. [i] and [2]. For the computation the under water hull of the dredger barge has to be represented by plane facet elements. In the centre of each facet el-ement a source is located in which the pressures are computed. The

distribution of the plane facet elements is shown in Figure ii. In

Figure 5 the frequency dependent added mass and damping coefficients for the principal motions, respectively along the x, z and e-axis

(with regard to the C.o.G.) are presented. In Figure 6 the wave

ex-citing forces and moment with regard to C.o.G. are given. The coef-ficients of the restoring forces can be split up in hydrostatic re-storing force coefficients and spud rere-storing force coefficients or

in matrix form: c c c Ox Oz 00 3E1 c -B s 1 c xO 3 s i C Ox s i c00 - (i inwhich: EI 1,050,000 ton.m2 i = 17.14 m KG = 5.33 in

The matrix of the hydrostatic restoring force coefficient is deter-mined in the usual way. For the determination of the matrix of the

spud restoring force coefficients use can be made of Figure 1. For the system in moored condition the cutter ladder has to be deleted. The spud guiding system is assumed to be a free vertical spud slid-ing system (no friction). By linearizslid-ing the spud restorslid-ing force coefficient, assuming that f.O « l,we obtain:

c0 co Co

_{coe_}

Hyostatic

Spud restoring

restoring force force

coefficients coefficients

[ton/rn]

[ton/rad.]

[ton .m/m]

[ton.m/rad.]

The matrix of the restoring force coefficients is as follows:

c c xx c c zx xz zz c c zEi = c c c XXh c ZXh XZh ZZh c XOh c ZOh + c c xx zx c s c s xz s zz s c xO s c zO s c c

c

xx xz x® c c c zx zz zO c0 c0 c00 O O 01,355.7 0 0 0 0 557131.0 + 625.6 0 -12,9143.1 0 0 0 -1943.1 0 267793.O

(9)

MODEL

The computed motion respone functions and the reponse amplitude

operator of the spud. force are shown in Figure

8.

In this figure a]o. the eured i'esponse function-s of the motions and the spud

ore F

are presented.

Discussion of the Results

th'ave

igtspplied it can be concluded that the

mo-.tions of the dredger and the spud forces are predicted correctly. The shape of the amplitude response operator of the pitch and surge motion and of the spud force shows maximum values at the frequency

= 0.68

rad./sec.

Extinction tests in surge and pitch direction result in a pitch rotation around the spud ball-joint connection at the sea bottom.

-This behaviour is due to the strong coupling in the mooring system. The natural frequency of this motion amounts to

0.68

rad./sec. (9.2 sec.), which corresponds with the peak frequency of the mentioned amplitude response operators. Since in realistic sea states these wave frequencies often occur large forces and moments on the spud andspud carriage can be expected.

OPERATIONAL CONDITION

Discussion of Model Test Results

- In order to have a better understanding of the behaviour of the

dredger, time records of the measurements in oreratisnal conditions in regular head waves are shown in Figures 9 and 10. The results re-veal that for the larger wave periods the system is strongly

non-linear. -The cutter head comes free from the breach, while impact

loads occur when it falls back. The impact loads influence the dredger motions. Also for the larger wave periods the spud force shows large amplitude, high frequency components. The frequency co-incides with the "natural pitch and surge period" of the system. The results of small amplitude extinction tests in the longitudinal centre plane show a combined "pitch-surge natural frequency"

of 1.61

rad./sec. (3.9 sec.). These natural frequencies will 'ce generated by

:the impact loads on the cutter head and will 'ce transient by nature.

tIn Figure 11 the behaviour of the dredger in larger head waves dur-ing one wave period is shown schematically.

In head waves at the wave period of 6 sec. the motions and the

mooring forces are relatively small. In short beam waves, however, relatively large loads on the spud and high impact icads on the cut-ter head occur as is indicated in Figure 12. Both loads work in longitudinal direction perpendicular to the wave direction. This must be contributed to the heave motion of the dredger and enhancement

effects of the combined pitch-surge natural frequency

FUTURE DEVELOPMENTS OF COMEUTATIONS

For the operational condition the restoring force at the cutter

head will be -a non-linear function of the cutter head displacement.

In order to solve the non-linear behaviour of the dredger in

op-erational conditions by computations it is necessary to formulate a

(10)

and

C'TEL

= m (w)

_J

K (t) sin wt dt

xx xx w xx

Examples of these computations for moored objects for more degrees of freedom have been given by Van Oortmerssen and Wichers, see Ref.

[2], [5]. Using this time domain approach it is expected that the operational condition can be solved numerically.

forces and motions. The set of equations of motions has to be solved in the time domain. The problem then is to describe the hydrodynamic

eaction forces due to arbitrarily, in time varying, ship motions. To solve this problem the approach of Cunimins, see Ref. [3], can be

'followed. Cummins describes an arbitrary motion as a succession of small impulsive displacements. His basic assumption is that at any time the total fluid reactive force is the sum of the reactions to the individual impulsive displacements, each reaction being calcu-lated with an appropriate time lag from the instant of the corre-sponding impulsive motion. Using the approach of

Cìn'rqins

and

consid-ering as an example the equation of motion in the time domain based on Newton's law of dynamics for the system with one degree of free-dom the formulation is as follows:

t

nix -m' .x -

f

K (t-T)x(T) dT +

xx xx

Hydrodynamic reaction forces

-c .x -F(x) +F (w) sin(wt+s

XX

_H

xa X

Hydrostatic non-linear Wave

restoring mooring exciting force restoring force

force

in which: in = mass of the dredger

ml = frequency independent added mass coefficient

K retardation function

Xx

e = linear hydrostatic restoring coefficient xx

F(x) non-linear restoring force caused by any possible non-linear load-displacement characteristic con-cerning spud and cutter head

F = amplitude of the steady oscillatory wave exciting force at frequency w

= phase angle with regard to wave

According to Ogilvie,see Ref. [14], the retardation function and the

inertia coefficient are related to the frequency dependent damping

and added mass:

K (t) =

_f

b (w) cos wt dt)

XX TI XX

(11)

-t i.

CONCLUSIONS _{::. ;.}

1. 1n regular head. waves and in rocky soil the behaviour of the cut-ter suction dredger in moored condition differs entirely from that in operational condition. In moored condition large loads on the spud can be expected, while in operational condition relativ-ely small spud loads in combination with relativrelativ-ely high impact loads on the cutter head can occur.

2. In head waves and in rocky soil the moored condition can be treated as a linear system. Computations in the frequency donain show that the motions of the dredger and the spud forces are pre-dicted well by the diffraction theory.

3. I is expected that both the frequency domain and the time domain computations (respectively concerning linear and non-linear

sys-tems) applied to cutter suction dredgers operating in waves will be an aid to study the influence of the soil parameters or systei parameters on the motions and the spud and cutter head forces.

REFERENCES

[i] Boreel, L.J., "Wave Action on Large Offshore Structures", Conference on Offshore Structures, Inst. of Civil Engineers,

London, 19711.

Oortmerssen, G. van, "The Motions of a Ship in Shallow Water", N.S.M.B. Publication No. 510, Wageningen,

_1976.

Cummins, W.E., "The impulse Response

Function

and Ship Motions",

Department of the Navy, David Taylor Model Basin, Retort No.

1661,

Washington, D.C., October

_1962.

[11] Ogilvie, T.F., "Recent Progress toward the Understanding and

Prediction of Ship Motions", gth Syrstosium on Naval Hydrody-namics. Bergen, Norway,

1964.

[5]

Wichers, J.E.W., "Slowly Oscillating Mooring Forces in Single Point Mooring Systems", Second International Conference cn

On the forces on a cutter suction dredger in waves

J

i

Tehi

e oc! e', Cet

DCU-

-'.

rduct.n hc:

2i1

...

. ...:.

Swing Side Wires.,.

:::-''. ...

8, 9,

9.0

mm

mm

0.19

0.91

0.19

-0.91

rductir

-:

:fl

(m-1-a )+a .+a .0+b .+b .+b

.é+

+c .x+c .z+c .O=F

sin(wt+c

.+(m+a )+a .®+b

±+b .+b

.6+

+c .x+c .z+c .0=F

sin(wt+c

+c .x+c .z+c .G=M

Oz

coe_

Hyostatic

c

8.

ore F

th'ave

= 0.68

0.68

of 1.61

J

Cìn'rqins

f

H

f

-t i.

1976.

Function

1661,

1962.

1964.

[5]

auxiliary spud

spud with carriage

Fig. i

Cutter suction

dredger with spud

and

o

c'j

dimensions are given

in metres for the

full

scale

Fig. 2

Barge

dimensions

C.o.G.

5.33

L 1L

34.88

16.00

74.67

H

dimensions

are given

_{:::-''. ...}

_-:

_.é+

_{coe_}

_J

_H

_f

_1976.

_1962.

_{Cutter suction}

_{dredger with spud}

_and

_{in metres for the}

_full

_scale

_16.00

_{in metres for the full}

_scale

_{Test set-up and sign}

_convention

_1'-or

_sy

_{the principal directions of motion}